====== Trimming implicit surfaces ======
{{frep:tn_ms0_w.gif?170nolink}}**A** {{frep:tn_mss_w.gif?170nolink}}**B** {{frep:tn_mst_w.gif?170nolink}}**C**

A = B \ C

A is a trimmed implicit surface (2-manifold with boundary) - set difference of B and C,\\
B is a spherical surface,\\
C is a solid constructed by sweeping and set-theoretic operations.

{{frep:tr_bl1_w.gif?noplink}}**D** {{frep:tr_bl0_w.gif?nolink}}**E**

D = E \ C

D is a trimmed blobby surface - set difference of E and C,\\
E is a blobby surface.

{{frep:tr_head0.jpg?200&nolink}}**H** {{frep:tr_head1.jpg?200&nolink}}**F**

F = H \ C

This work was inspired by art works of [[http://www.worldofescher.com/gallery/|M.C. Escher]], namely "Sphere Spirals" (1958) (see them redesigned in the top figure) and "Bond of Union" (1956), showing spiral shaped surface sheets cut of a sphere and human head surfaces.

{{frep:tr_fon_carr.jpg?190x200&nolink}}**K** {{frep:tr_fon_trim.jpg?223x200&nolink}}**L**\\
{{frep:tr_fon2.jpg?419x220&nolink}}**M**

M = K \ L

G. Pasko, A. Pasko "Trimming implicit surfaces", The Visual Computer, vol. 20, No. 7, 2004, pp. 437-447.\\
Electronic version: [[http://hyperfun.org/Trim_TVC04.pdf|PDF (871 K)]]

B. Schmitt, A. Pasko, G. Pasko, T. Kunii , Rendering trimmed implicit surfaces and curves, AFRIGRAPH 2004 Proceedings, publication of ACM SIGGRAPH, 2004, pp. 7-13.